Academic scheduling is a complex and time-consuming process that requires balancing multiple constraints such as faculty availability, subject distribution, and classroom capacity. Manual timetable preparation often results in scheduling conflicts, uneven workload distribution, and administrative inefficiency. This research proposes AutoTimely, an intelligent, automated timetable generator designed to address these challenges using optimization algorithms. The system integrates Genetic Algorithm (GA) and Constraint Satisfaction Problem (CSP) techniques to generate efficient, conflict-free schedules. The GA component handles optimization through selection, crossover, and mutation operations, while CSP ensures hard constraints are satisfied. The proposed system is developed using Python (Flask), HTML/CSS/JavaScript, and JSON for data storage. Experimental validation using real institutional data demonstrated that AutoTimely reduced scheduling time by 40% and minimized conflicts to less than 2%. The study concludes that hybrid optimization models can significantly enhance academic timetable generation, providing a scalable and efficient solution for educational institutions

In response to the demand for integrated and cost-efficient production systems, this study addresses a lexicographic bi-objective scheduling problem with budget constraints in distributed production–transportation–assembly flow shop systems. The first objective is to minimise makespan under heterogeneous resource and budget limitations across multiple sites; the second is to minimise total transportation and assembly costs without exceeding the optimal makespan. This yields a two-stage sequential scheduling framework. In Stage 1, a reduced mixed-integer linear programming (MILP) model is first solved to determine the minimum feasible budget, followed by three alternative formulations – Manne-based MILP, position-based MILP, and constraint programming (CP) While exact models solve small instances, they are intractable for realistic scales. To enhance scalability, we develop logic-based Benders decomposition (LBBD) and branch-and-check (BCH) variants with bound-strengthening strategies. In Stage 2, MILP, CP, and LBBD methods minimise costs subject to the makespan. Here, a CP warm start is embedded in LBBD to accelerate convergence. Computational experiments show that decomposition-based methods substantially outperform monolithic models. In Stage 1, LBBD achieves clear advantages over MILP and CP; in Stage 2, LBBD reduces costs by 4.04% and 13.26% on small and large instances, respectively. Sensitivity analyses further provide managerial insights for budget-aware scheduling in distributed networks.

ABSTRACT Frigate shipbuilding requires meticulous scheduling due to unique construction processes, involving numerous tasks and limited resources. Current strategies, particularly those involving block erection on slipways, face bottlenecks in hull assembly due to resource constraints. This study addresses these challenges through an extended formulation of the Flexible Job-Shop Scheduling Problem with Assemblies (FJSP-A), incorporating limited workshop capacity and a fixed block-erection strategy. We evaluate the performance of exact and heuristic solution methods, comparing a strengthened constraint programming (CP) model, a holistic mixed-integer linear programming (MILP) formulation, a MILP-based decomposition approach from the literature, and two adapted metaheuristics, a genetic algorithm (GA) and a differential evolution (DE) strategy. While CP consistently delivers the best solutions across objectives, large lower-bound gaps remain in the most complex instances. Metaheuristics, particularly the GA with a sequencing-focused encoding, provide competitive alternatives when faster approximate solutions are required or when problem size or available budget limits the use of exact methods. The results offer practical guidance for selecting optimisation strategies in shipbuilding environments and highlight research avenues for integrating enhanced heuristics or multi-objective approaches into resource-constrained assembly scheduling.

In real-world production, a few operations of a job may do not follow precedence constraints. However, classical flexible job shop scheduling problem (FJSP) typically assume operations sequence is fixed. Therefore, this study investigates the FJSP with discrete operation sequence flexibility (FJSPDS), aiming to minimise the makespan. First, a novel constraint programming (CP) model is proposed to obtain optimal solutions. Then, a matheuristic and imitation learning-driven evolutionary algorithm (MILEA) is developed to effectively solve large-scale instances. The MILEA includes three key components: (1) a matheuristic-based hybrid initialization method that enhances the quality of the initial population by utilising the mathematical model to explore better operation sequencing; (2) an imitation learning-assisted local search mechanism that adaptively selects seven critical path-based operators to refine solutions; and (3) a CP-assisted evolutionary operator that overcomes the limitations of traditional encoding-decoding schemes and broadens the exploration of the solution space. Experiments are performed on 110 benchmark instances, and experimental results show that the proposed CP model proves 60 optimal solutions and improves 86 best-known solutions compared with existing models. Meanwhile, MILEA proves 60 optimal solutions and improves 52 best-known solutions compared with existing state-of-the-art algorithms.

Mixed-integer programming and constraint programming approaches for precast concrete flowshop scheduling with multiple production lines

Constraint Programming for AGV and Machine Integrated Scheduling Problem in Flexible Manufacturing System

Corporate travel procurement is a multi-objective, constraint-dense decision domain spanning strategic supplier portfolio selection, travel policy design, and operational disruption response. Classical methods—mixed-integer programming (MIP), constraint programming, metaheuristics, and machine learning—deliver strong results but face scaling and responsiveness challenges as procurement objectives broaden to include compliance, traveler experience, sustainability, and resilience. Quantum optimization methods, particularly quantum annealing and gate-based variational algorithms (e.g., QAOA), have been proposed for combinatorial problems with binary decisions and complex interaction terms. Yet empirical evidence across optimization domains often shows classical solvers match or exceed quantum approaches on meaningful instance sets, motivating a hybrid quantum–classical posture rather than replacement. This paper formalizes quantum-enhanced travel procurement as a hypothesis-driven, hybrid decision-support approach in which quantum routines contribute to solution search, diversification, or time-to-decision for selected combinatorial cores. We present canonical procurement formulations, show explicit mappings to QUBO/Ising models, and propose hybrid architectures for supplier portfolio design, airline share allocation under commitments, policy parameter tuning, and disruption re-accommodation. To strengthen accessibility and rigor, we provide (i) a worked QUBO example with explicit coefficients and variable counts; (ii) an operational benchmark protocol with representative instance sizes, solver baselines, runtime assumptions, and statistical reporting; and (iii) an enterprise governance view including post-quantum cryptography readiness across vendor integrations.

In the current media environment, with distracted attention and information overload, health information is often difficult to turn into actual protective behavior. Based on HBM theory, a narrative mechanism of "construct-visual grammar" mapping and constraint solving was created, and a complete system of data collection, construct estimation , parametric visual design, WebGL/Canvas rendering, and A/B evaluation was established. Bootstrap and permutation tests were performed, and means, 95% confidence intervals, and effect sizes were reported, which were calibrated together with reliability curves and ECE assessments. Compared with static infographics and generic templates, HBM visualization significantly improved correct understanding, protection intention, click-through rate, and user dwell time. It also achieved the minimum ECE value and a high adoption area under the balanced narrative type. The system maintained scalability from 1080p to 4K and within the range of 30 to 60 seconds. The overlap between chronic disease, vaccination, and mental health scenarios was high. HBM-based visual narrative constructs an explainable, measurable, and easily deployable strategic framework for health communication. While complying with regulations and ensuring accessibility, it improves audience understanding and behavioral tendencies, while demonstrating a strong ability to migrate across domains.

Abstract Object-oriented programming is the dominant paradigm for general-purpose programming languages. While several attempts have been made to introduce object models into constraint modelling languages, these often have restrictions in terms of their expressivity, are not available in mainstream modelling languages, or are incompatible with modern solving technology. To address these challenges, this paper identifies essential requirements for expressive and elegant object-oriented constraint modelling. We propose an object model that supports decision variables of object type, objects referring to other objects, and, crucially, variable sets of objects, whose cardinality is decided by the solver. The object model is presented as an extension of the MiniZinc modelling language that can be translated into standard MiniZinc. A number of examples and a case study demonstrate the viability of the approach.

Solving logic-based benders decomposition master problems with constraint programming and domain-independent dynamic programming

We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class \({\mathcal{C}}\) of finite structures that can be expressed in MSO and is closed under homomorphisms, and for all \(\ell,k\in{\mathbb{N}}\) , there exists a canonical Datalog program \(\Pi\) of width \((\ell,k)\) in the sense of Feder and Vardi. The same characterisations also hold for Guarded Second-order Logic (GSO), which properly extends MSO. To prove our results, we show that every class \({\mathcal{C}}\) in GSO whose complement is closed under homomorphisms is a finite union of constraint satisfaction problems (CSPs) of \(\omega\) -categorical structures. The intersection of MSO and Datalog is known to contain the class of nested monadically defined queries (Nemodeq) ; likewise, we show that the intersection of GSO and Datalog contains all problems that can be expressed by the more expressive language of nested guarded queries (GQ \({}^{+}\) ) . Yet, by exploiting our results, we can show that neither of the two query languages can serve as a characterization, as we exhibit a CSP whose complement corresponds to a query in the intersection of MSO and Datalog that is not expressible in GQ \({}^{+}\) .

\(\boldsymbol{\Pi_2^P}\) vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem

Despite significant advances in characterizing the highly nonconvex landscapes of constraint satisfaction problems, the good performance of certain algorithms in solving hard combinatorial optimization tasks remains poorly understood. This gap in understanding stems largely from the lack of theoretical tools for analyzing their out-of-equilibrium dynamics. To address this challenge, we develop a system of approximate master equations that capture the behavior of local search algorithms in constraint satisfaction problems. Our framework shows excellent qualitative agreement with the phase diagrams of two paradigmatic algorithms: Focused Metropolis Search (FMS) and greedy-WalkSAT (G-WalkSAT) for random 3-SAT. The equations not only confirm the numerical observation that G-WalkSAT's algorithmic threshold is nearly parameter-independent but also successfully predict FMS's threshold beyond the clustering transition. We also exploit these equations in a decimation scheme, demonstrating that the computed marginals encode valuable information about the local structure of the solution space explored by stochastic algorithms. Notably, our decimation approach achieves a threshold that surpasses the clustering transition, outperforming conventional methods like Belief Propagation-guided decimation. These results challenge the prevailing assumption that long-range correlations are always necessary to describe efficient local search dynamics and open a path to designing efficient algorithms to solve combinatorial optimization problems.

Purpose This paper introduces a novel algorithm, the Differential Evolution-based Backtracking Search Algorithm (DEBSA), designed to address the computational limitations of the Backtracking Search Algorithm (BSA) for complex constraint satisfaction problems. Design/methodology/approach DEBSA merges the core structure of BSA with three innovative mutation strategies derived from Differential Evolution (DE). These strategies focus on directing a random individual toward a historical individual and utilizing a random individual in conjunction with a perturbation vector as well as leveraging a historical best position with two perturbation vectors. Furthermore, DEBSA incorporates a unique crossover mechanism for combining solutions and a strategy selection approach to dynamically choose the most suitable mutation strategy during the search process. Findings DEBSA’s performance is evaluated on constrained optimization problems and systems of nonlinear equations. The results demonstrate exceptional performance, particularly in terms of convergence speed, surpassing traditional benchmark evolutionary algorithms. DEBSA exhibits a high success rate in achieving globally optimal solutions. Originality/value The proposed DEBSA offers a potentially efficient solution for tackling general optimization challenges in engineering design and solving nonlinear equations in applied mathematics due to its enhanced performance and ability to find global optima.

Abstract Background Manual emergency department (ED) rostering is labour‐intensive and prone to inconsistency. We developed and implemented an artificial intelligence (AI)‐assisted rostering system that combined large language model (LLM)–supported coding with a constraint solver. This study describes its development, implementation and lessons learnt from real‐world use. Methods This implementation‐science project involved a clinician‐led team building a Python‐based rostering programme using ChatGPT for code generation and Google OR‐Tools for optimisation. Development followed iterative cycles of prototyping, testing and user feedback. The solver first generated a basic roster backbone of A (morning), P (afternoon), N (night) and O (off) duties under fixed, adjustable and soft constraints. A post‐processing module then translated these into duty subtypes to improve coverage. Implementation outcomes included efficiency, roster quality and coverage, assessed by workload balance, reduction of unfavourable patterns, fairness metrics and staff feedback. Results The system produced feasible rosters across five consecutive monthly cycles and reduced drafting time by over 90%. Roster quality improved with more balanced coverage among ranks, fairer duty and off‐day allocation and about 30% fewer unfavourable patterns. The model maintained consistent rest rules and equitable workload distribution. Early phases required constraint tuning and human verification, which decreased as the model stabilised. Informal feedback noted improved predictability, fairness and coverage stability. Conclusion An AI‐assisted rostering system was successfully developed and deployed in a clinical setting through iterative human–AI collaboration. LLM‐assisted programming enabled nonprogrammers to create adaptable operational tools. The modular backbone–post‐processing design allows replication in other EDs with minimal modification.

Constraint programming models for serial batch scheduling with minimum batch size

Purpose This study aims to enhance construction scheduling through a computational methodology that enables structured input preparation, constraint formulation and combinatorial task analysis to improve schedule feasibility, automation and optimization Design/methodology/approach The proposed methodology integrates building information modeling (BIM), enhanced planning and scheduling (EPS), a structured scheduling approach and constraint programming (CP) to enhance computational and combinatorial scheduling. BIM data is automatically extracted and enriched with material quantities, spatial breakdowns and task types, then structured using EPS into labor-hour–based units and spatial zones. These structured inputs feed into a CP model incorporating precedence logic, resource constraints and execution priorities to generate the construction schedule. Moreover, constraint modification and EPS-driven combinatorial analysis enable alternative scheduling and scenario evaluation. Findings The methodology was applied to a multi-section residential project, resulting in a feasible and optimized construction schedule. The CP model optimized resource use and duration based on the objectives while maintaining logical sequencing, with automated BIM-EPS input reducing manual effort. The schedule was automatically generated based on the predefined constraints and consistency was confirmed using Kendall’s Tau-b correlation. Originality/value This study presents a novel integration of BIM, EPS and CP to advance logic-based and computational scheduling. A key contribution of this study is the implementation of advanced scheduling by facilitating constraint formulation through the EPS methodology and enriched BIM data integration. This approach enables schedule feasibility analysis, improves consistency and addresses limitations of constraint- and logic-based methods through structured input and formalized constraints. By automating the extraction and structuring of data for CP, it reduces some manual effort in data preparation and supports optimization though initial setup and predefined constraints.

Futoshiki is a computationally hard problem belonging to the Latin Square Completion-type Puzzles. It is played on a partially filled n×n grid that may include inequality constraints between cells. The objective is to complete the grid such that each row and column contains the integers from 1 to n exactly once, while also satisfying all inequality constraints. In this work, we propose FutoshikiACO, an Ant Colony Optimization-based algorithm to solve Futoshiki instances of fixed size. We evaluate the performance of this stochastic method through computational experiments. Compared to existing deterministic approaches, FutoshikiACO explores a significantly reduced search space. Our results not only demonstrate the inherent complexity of the Futoshiki problem but also highlight the types of instances where ant colony-based metaheuristics are particularly effective in solving such constraint satisfaction problems.

A fundamental result in the study of graph homomorphisms is Lovász's theorem that two graphs are isomorphic if and only if they admit the same number of homomorphisms from every graph. Cai and Govorov capped a line of work extending Lovász's result to more general types of graphs by showing that it holds for graphs with vertex and edge weights from an arbitrary field of characteristic zero. Counting graph homomorphisms is a counting constraint satisfaction problem (#CSP) parameterized by a single constraint function of arity two. In this work, we extend Lovász's theorem to general #CSP by showing that any two sets $\mathcal{F}$ and $\mathcal{G}$ of constraint functions are isomorphic if and only if they are #CSP-indistinguishable -- that is, the partition function value of any #CSP instance is unchanged when we replace the functions in $\mathcal{F}$ with those in $\mathcal{G}$. We give two very different proofs of this result. First, we give a proof for complex-valued constraint functions using the intertwiners of the automorphism group of a constraint function set, a concept from the representation theory of compact groups, in the style of Mančinska and Roberson's proof of the equivalence between quantum isomorphism and homomorphism indistinguishability over planar graphs. Second, we demonstrate the power of the simple Vandermonde interpolation technique of Cai and Govorov by extending it to general #CSP, giving a constructive proof for constraint functions with entries from any field of characteristic zero.

Institutions of higher education must balance multiple, often conflicting objectives when setting admission targets for their academic programs. In this paper, we introduce a recommendation system that integrates Constraint Satisfaction Problem (CSP) techniques, goal programming, and Equity Theory to optimize student assignments. Our model strictly enforces hard constraints—such as faculty-hour limits and classroom capacities—while accommodating soft constraints—such as government quotas and institutional preferences—through adjustable penalty functions. Evaluations against static and heuristic benchmarks show that our approach maintains enrollment at 85–90% of total capacity, markedly reducing both the frequency and severity of constraint violations. Furthermore, an average Gini coefficient of 0.067 demonstrates a fairer distribution of seats across programs. Over five simulated admission cycles, institutions employing this recommender achieve substantial compliance improvements within four years, striking an effective balance between rapid constraint adherence and stable enrollment figures. These results confirm that our system offers a practical, data-driven solution for flexible and equitable enrollment management in resource-limited higher-education settings.